Does HDR sky resolution change a lighting?
Resolution of HDRi doesn't change strength of light too much.
Resolution have an influence on sharpness of shadows.
Probably not visible too much between 2K / 8K, but for lightning with 256px result visibly differs (see end of cube shadow). Small sharp point as light source (like sun) produce sharp shade, in small images it can be just a pixel, but usually is divided into several and also small image means bigger pixels in environment.
You can test it by your self if it matters in your case. Render them and if not noticable you can even try blend renders by Difference type to see per pixel differences.
Surprisingly for me it affects noise in render too.
Probably texture shoots light per pixel, so more pixels - more light rays ...? Anyway you would have to render with more samples fór lowres HDRi, than with highres HDRi, to get same quality.
In those two images I changed only HDRi texture resolution ... same samples.
256 px

8 K

Bigger issue can be a reflection.
... in case you have any visible in render.
256px / 8K

In case you need lowres environment HDRi texture for it's size, people use jpg version of HDRi in highres for just reflections. World node tree - Light path &gt; Reflection Rays as factor.


I can't find the specific article of Greg Zaal, but you can check those as well Link1 or Link2.